Question

reason inductively explain how you could find the area of the three - quarter circle shown. to find the area, multiply the area of the entire circle by —. 6 cm

Explanation:

Step1: Determine the fraction of the circle

A full circle is \( 360^\circ \). The missing sector is a right angle (\( 90^\circ \)), so the remaining angle is \( 360^\circ - 90^\circ = 270^\circ \). To find the fraction of the circle, divide the remaining angle by \( 360^\circ \): \( \frac{270^\circ}{360^\circ} = \frac{3}{4} \).

Step2: Relate to area calculation

The area of a full circle is \( A = \pi r^2 \). For the three - quarter circle, we multiply the area of the full circle by the fraction we found (\( \frac{3}{4} \)).

Answer:

\(\frac{3}{4}\)